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Theorem axext4 2439
 Description: A bidirectional version of Extensionality. Although this theorem "looks" like it is just a definition of equality, it requires the Axiom of Extensionality for its proof under our axiomatization. See the comments for ax-ext 2435 and df-cleq 2449. (Contributed by NM, 14-Nov-2008.)
Assertion
Ref Expression
axext4
Distinct variable groups:   ,   ,

Proof of Theorem axext4
StepHypRef Expression
1 elequ2 1823 . . 3
21alrimiv 1719 . 2
3 axext3 2437 . 2
42, 3impbii 188 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  A.wal 1393 This theorem is referenced by:  axc11next  31313 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-ex 1613
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